Using boundary conditions appropriate to the Local Cloud embedded in the Local Bubble, the evaporation of the cloud is modeled assuming steady flow. Included in the model are the effects of radiative cooling and nonequilibrium ionization structure in the interface, and pressure support and heat conduction inhibition due to the magnetic field. The soft X-ray and EUV emission from the interface are calculated and compared with observations. It is found that the emission in the softest X-ray band, the Be band, is harder than that calculated for an equilibrium, normal abundance, 10 to the 6th K plasma. Column densities of C IV, N V, O VI, Si IV, and Si III in the interface are calculated. The column density for O VI is found to be very close to observed values for nearby stars, while all others are too small to contribute significantly to observed values. The ionization of the Local Cloud due to radiation from the interface is calculated. It is found that a significant amount of ionizing radiation is produced, dominating all other known sources. The hardness of the emission, however, results in ionization of helium as well as hydrogen. Thus, the type of boundary modeled cannot explain the ionization of the very local interstellar medium inferred from solar backscatter measurements.